Practical Data Wrangling With R
Day One
The Tidyverse
* __ _ __ . o * .
/ /_(_)__/ /_ ___ _____ _______ ___
/ __/ / _ / // / |/ / -_) __(_-</ -_)
\__/_/\_,_/\_, /|___/\__/_/ /___/\__/
* . /___/ o . * We are going to be working around in the tidyverse for a good chunk of our time together. The whole point of the tidyverse is to offer a grammer of verbs. It is going to help us in a lot of the situations that we are going to be seeing.
Another great feature of the tidyverse is the pipe: %>%
It does the same thing as the Unix |, but | in R is an or operator.
With all of the glowing praise for the tidyverse, we are still going to see some base R. Sometimes, it will demonstrate great reasons for using the tidyverse. In other situations, it will help you to not be afraid to use it when situations arise.
Some Demonstrations
Summary Tables
library(ggplot2)
plotDat = aggregate(diamonds$cut, by = list(cut = diamonds$cut), FUN = length)
colnames(plotDat)[2] = "n"
plotDat cut n
1 Fair 1610
2 Good 4906
3 Very Good 12082
4 Premium 13791
5 Ideal 21551Visual
ggplot(plotDat, aes(x = cut, y = n)) +
geom_point(aes(size = n)) +
theme_minimal()
(Im)Proper Plotting
Look at help(mtcars) and check out the variables. Can you spot what is wrong with this plot?
ggplot(mtcars, aes(x = wt, y = mpg, color = am)) +
geom_point() +
theme_minimal()
Proper Plotting
The plot below is likely better.
library(dplyr)
mtcars$amFactor = as.factor(mtcars$am)
ggplot(mtcars, aes(x = wt, y = mpg, color = amFactor)) +
geom_point() +
theme_minimal()
Pipes: Making Life Easier
Recall some of the things that we just saw:
plotDat = aggregate(diamonds$cut, by = list(cut = diamonds$cut), FUN = length)
colnames(plotDat)[2] = "n"
ggplot(plotDat, aes(x = cut, y = n)) +
geom_point(aes(size = n)) +
theme_minimal()This is somewhat tricky code. We have to create a new object with the oft-muddy aggregate and reset a column name (by magic number in an index, no less).
This can be made much easier with dplyr:
diamonds %>%
group_by(cut) %>%
summarize(n = n()) %>%
ggplot(., aes(x = cut, y = n)) +
geom_point(aes(size = n)) +
theme_minimal()
It isn’t a reduction in lines, but it is certainly clearer and follows a more logical thought process. This is the whole point of the tidyverse (and dplyr specifically) – allowing you to write how you would explain the process.
As an added bonus, we don’t need to create a bunch of different objects to do something simple.
We can see that dplyr will also make the plot for am easier.
mtcars %>%
mutate(am = as.factor(am)) %>%
ggplot(., aes(x = wt, y = mpg, color = am)) +
geom_point() +
theme_minimal()
On Code Golf
You will often notice that a dplyr chunk might take a few more lines to work through than base R alone – don’t consider this as a bad thing. There will be many times in this course and in your potential work that you might think that you need to use as few lines as possible. Resist this temptation. Sometime you need to break something up into many lines and create new objects – this ability is exactly why we use R!
Data Import
Importing data is often the easiest part (never too hard to import a nice .csv). Sometimes, though, we need some other strategies.
Delimited Files
Frequently, you will see nicely delimited text files that are not .csv files – these are often tab-delimited file, but they can take other forms.
read.table("https://download.bls.gov/pub/time.series/ce/ce.data.42a.RetailTrade.Employment",
header = TRUE, sep = "\t")Is the same as:
read.delim("https://download.bls.gov/pub/time.series/ce/ce.data.42a.RetailTrade.Employment")The read.table() function gives you added flexibility to specify many different parameters.
Examine the following file from SDC Platinum and read it in properly:
How did you do?
Did you notice anything about these files? They are not really very big, but they might have taken a little bit of time to read in. There have been times where people have commented that R is too slow on the read side. If you find you files are not being read quickly enough, you can try a few alternatives: readr data.table
Try the following:
readrTest = readr::read_delim("https://download.bls.gov/pub/time.series/ce/ce.data.42a.RetailTrade.Employment",
delim = "\t")dtTest = data.table::fread("https://download.bls.gov/pub/time.series/ce/ce.data.42a.RetailTrade.Employment",
sep = "\t")That SDC file that might have taken a few minutes will now take just a few seconds:
sdc = readr::read_delim("https://www3.nd.edu/~sberry5/data/sdcTest.txt",
delim = "^")Pretty awesome, right?
At times, you will get data in some proprietary format. That is when you need to turn to other places.
Excel
readxl::read_excel(path = "folder/fileName")What do we know about Excel workbooks? Check out the help on readxl and let me know our path forward.
SAS
haven::read_sas(data_file = "https://www3.nd.edu/~sberry5/data/wciklink_gvkey.sas7bdat")Stata
haven::read_dta(file = "https://www3.nd.edu/~sberry5/data/stataExample.dta")SPSS
We often see the -99 added as the missing value in SPSS (of course, there is no way that -99 would ever be an actual value, right?).
haven::read_spss(file = "https://www3.nd.edu/~sberry5/data/spssExample.sav",
user_na = "-99")HTML
Depending on your needs, reading an html table into R is getting to be too easy.
library(rvest)
cpi = read_html("http://www.usinflationcalculator.com/inflation/consumer-price-index-and-annual-percent-changes-from-1913-to-2008/") %>%
html_table(fill = TRUE)Things might get a bit tricky:
highest = read_html("https://en.wikipedia.org/wiki/List_of_highest-grossing_films") %>%
html_table(fill = TRUE)What is the return of this call?
rio
For many of these tasks, you can just use the rio package – you give it the file and it will do the rest!
rio::import("folder/file")Nested Structures
JSON
Web-based graphics started getting popular not too long ago. Generally, stats people were not using them, but web developer-type folks were. They needed a structure that would work well for the web and interact with their JavaScript-based graphics – thus, JavaScript Object Notation (JSON) was born. You will see JSON come out of many web-based interfaces.
There are a few JSON-reading packages in R, but jsonlite tends to work pretty well.
###optionsDataBrief
jsonTest = jsonlite::read_json(path = "https://www3.nd.edu/~sberry5/data/optionsDataBrief.json",
simplifyVector = TRUE)This is a very simple form of JSON. We are going to see a hairier verson of this data soon.
JSON Dangers
There is JSON and then there is JSON. You might find yourself some interesting data and want to bring it in, but an error happens and you have no idea why the read_json function is telling you that the file is not JSON.
Not all JSON is pure JSON! When that is the case, you will need to create pure JSON.
XML
It is getting to be a bit less common (still prevalent), but XML (eXtensible Markup Language) is another type of nested structure common on the web.
xml2::read_xml()Mass Reading
Everything we just learned is great and you will use them all in your data wrangling missions.
Fortunately (or unfortunately, depending on how you look at it), it is not the whole story – you will frequently be reading in many files of the same time.
If you have two files, you might be able to get away with brute force:
# DO NOT RUN:
myData1 = read.csv("test.csv")
myData2 = read.csv("test2.csv")Would you want to do this for 5 files? What about 100? Or 1000? I will answer it for you: no!
The chunks below introduce some very important functions. We are going to see lapply again – it is important that you learn to love the apply family!
# DO NOT RUN:
allFiles = list.files(path = "", all.files = TRUE, full.names = TRUE,
recursive = TRUE, include.dirs = FALSE)
allFilesRead = lapply(allFiles, function(x) read.csv(x, stringsAsFactors = FALSE))
allData = do.call("rbind", allFilesRead)You can also use rio:
# DO NOT RUN:
rio::import_list("", rbind = TRUE)Your Turn
- Take a look at this file:
- Determine how it should be read in.
- Summarize the data.
- Visualize the data in any way you wish!
The Grammar Of Data
One of the major aims of the tidyverse is to provide a clear and consistent grammar to data manipulation. This is helpful when diving deeper into the weeds.
Do you remember this?
highest = read_html("https://en.wikipedia.org/wiki/List_of_highest-grossing_films") %>%
html_table(fill = TRUE)What did we get out of this? It was a big list of data frames. If we are looking for only one thing and we know that it is the first thing, we have some options:
highest = highest[[1]]This is great for keeping the object at first and then plucking out what we want. If you want the whole thing to be together, though, we have even more options:
highest = read_html("https://en.wikipedia.org/wiki/List_of_highest-grossing_films") %>%
html_table(fill = TRUE) %>%
`[[`(1)And now we see why R mystifies people. What does is that bit of nonsense at the end. It is really just an index shortcut. Once you know how to use it, it is great; however, it will make you shake your head if you see it in the wild without knowing about it first.
This is where the benefit of tidyverse becomes clear.
highest = read_html("https://en.wikipedia.org/wiki/List_of_highest-grossing_films") %>%
html_table(fill = TRUE) %>%
magrittr::extract2(1)Or…
highest = read_html("https://en.wikipedia.org/wiki/List_of_highest-grossing_films") %>%
html_table(fill = TRUE) %>%
purrr::pluck(1)Do be careful, though, because we can have some issues in function masking and pluck from purrr does something very different than pluck from dplyr.
Someone try it and tell me what happens!
Selecting
Base
There are many ways to select variables with base R:
mtcars[, c(1:5, 7:8)]
keepers = c("mpg", "cyl", "disp", "hp", "drat", "qsec", "vs")
mtcars[, keepers]
mtcars[, c("mpg", grep("^c", names(mtcars), values = TRUE))]You can also drop variables:
mtcars[, -c(1:2)] disp hp drat wt qsec vs am gear carb amFactor
Mazda RX4 160.0 110 3.90 2.620 16.46 0 1 4 4 1
Mazda RX4 Wag 160.0 110 3.90 2.875 17.02 0 1 4 4 1
Datsun 710 108.0 93 3.85 2.320 18.61 1 1 4 1 1
Hornet 4 Drive 258.0 110 3.08 3.215 19.44 1 0 3 1 0
Hornet Sportabout 360.0 175 3.15 3.440 17.02 0 0 3 2 0
Valiant 225.0 105 2.76 3.460 20.22 1 0 3 1 0
Duster 360 360.0 245 3.21 3.570 15.84 0 0 3 4 0
Merc 240D 146.7 62 3.69 3.190 20.00 1 0 4 2 0
Merc 230 140.8 95 3.92 3.150 22.90 1 0 4 2 0
Merc 280 167.6 123 3.92 3.440 18.30 1 0 4 4 0
Merc 280C 167.6 123 3.92 3.440 18.90 1 0 4 4 0
Merc 450SE 275.8 180 3.07 4.070 17.40 0 0 3 3 0
Merc 450SL 275.8 180 3.07 3.730 17.60 0 0 3 3 0
Merc 450SLC 275.8 180 3.07 3.780 18.00 0 0 3 3 0
Cadillac Fleetwood 472.0 205 2.93 5.250 17.98 0 0 3 4 0
Lincoln Continental 460.0 215 3.00 5.424 17.82 0 0 3 4 0
Chrysler Imperial 440.0 230 3.23 5.345 17.42 0 0 3 4 0
Fiat 128 78.7 66 4.08 2.200 19.47 1 1 4 1 1
Honda Civic 75.7 52 4.93 1.615 18.52 1 1 4 2 1
Toyota Corolla 71.1 65 4.22 1.835 19.90 1 1 4 1 1
Toyota Corona 120.1 97 3.70 2.465 20.01 1 0 3 1 0
Dodge Challenger 318.0 150 2.76 3.520 16.87 0 0 3 2 0
AMC Javelin 304.0 150 3.15 3.435 17.30 0 0 3 2 0
Camaro Z28 350.0 245 3.73 3.840 15.41 0 0 3 4 0
Pontiac Firebird 400.0 175 3.08 3.845 17.05 0 0 3 2 0
Fiat X1-9 79.0 66 4.08 1.935 18.90 1 1 4 1 1
Porsche 914-2 120.3 91 4.43 2.140 16.70 0 1 5 2 1
Lotus Europa 95.1 113 3.77 1.513 16.90 1 1 5 2 1
Ford Pantera L 351.0 264 4.22 3.170 14.50 0 1 5 4 1
Ferrari Dino 145.0 175 3.62 2.770 15.50 0 1 5 6 1
Maserati Bora 301.0 335 3.54 3.570 14.60 0 1 5 8 1
Volvo 142E 121.0 109 4.11 2.780 18.60 1 1 4 2 1dropVars = c("vs", "drat")
mtcars[, !(names(mtcars) %in% dropVars)] mpg cyl disp hp wt qsec am gear carb amFactor
Mazda RX4 21.0 6 160.0 110 2.620 16.46 1 4 4 1
Mazda RX4 Wag 21.0 6 160.0 110 2.875 17.02 1 4 4 1
Datsun 710 22.8 4 108.0 93 2.320 18.61 1 4 1 1
Hornet 4 Drive 21.4 6 258.0 110 3.215 19.44 0 3 1 0
Hornet Sportabout 18.7 8 360.0 175 3.440 17.02 0 3 2 0
Valiant 18.1 6 225.0 105 3.460 20.22 0 3 1 0
Duster 360 14.3 8 360.0 245 3.570 15.84 0 3 4 0
Merc 240D 24.4 4 146.7 62 3.190 20.00 0 4 2 0
Merc 230 22.8 4 140.8 95 3.150 22.90 0 4 2 0
Merc 280 19.2 6 167.6 123 3.440 18.30 0 4 4 0
Merc 280C 17.8 6 167.6 123 3.440 18.90 0 4 4 0
Merc 450SE 16.4 8 275.8 180 4.070 17.40 0 3 3 0
Merc 450SL 17.3 8 275.8 180 3.730 17.60 0 3 3 0
Merc 450SLC 15.2 8 275.8 180 3.780 18.00 0 3 3 0
Cadillac Fleetwood 10.4 8 472.0 205 5.250 17.98 0 3 4 0
Lincoln Continental 10.4 8 460.0 215 5.424 17.82 0 3 4 0
Chrysler Imperial 14.7 8 440.0 230 5.345 17.42 0 3 4 0
Fiat 128 32.4 4 78.7 66 2.200 19.47 1 4 1 1
Honda Civic 30.4 4 75.7 52 1.615 18.52 1 4 2 1
Toyota Corolla 33.9 4 71.1 65 1.835 19.90 1 4 1 1
Toyota Corona 21.5 4 120.1 97 2.465 20.01 0 3 1 0
Dodge Challenger 15.5 8 318.0 150 3.520 16.87 0 3 2 0
AMC Javelin 15.2 8 304.0 150 3.435 17.30 0 3 2 0
Camaro Z28 13.3 8 350.0 245 3.840 15.41 0 3 4 0
Pontiac Firebird 19.2 8 400.0 175 3.845 17.05 0 3 2 0
Fiat X1-9 27.3 4 79.0 66 1.935 18.90 1 4 1 1
Porsche 914-2 26.0 4 120.3 91 2.140 16.70 1 5 2 1
Lotus Europa 30.4 4 95.1 113 1.513 16.90 1 5 2 1
Ford Pantera L 15.8 8 351.0 264 3.170 14.50 1 5 4 1
Ferrari Dino 19.7 6 145.0 175 2.770 15.50 1 5 6 1
Maserati Bora 15.0 8 301.0 335 3.570 14.60 1 5 8 1
Volvo 142E 21.4 4 121.0 109 2.780 18.60 1 4 2 1Issues?
For starters, the magic numbers are a no-go. The keepers lines could work, but would be a pain if we had a lot of variables.
Let’s check this wacky stuff out where we want all variables that start with “age” and variables that likely represent questions (x1, x2, x3, …):
library(lavaan)
testData = HolzingerSwineford1939
names(testData) [1] "id" "sex" "ageyr" "agemo" "school" "grade" "x1"
[8] "x2" "x3" "x4" "x5" "x6" "x7" "x8"
[15] "x9" keepers = c(grep("^age", names(testData), value = TRUE),
paste("x", 1:9, sep = ""))
testData = testData[, keepers]Not only do we have another regular expression, but we also have this paste line to create variable names. It seems like too much work to do something simple!
While not beautiful, these are perfectly valid ways to do this work. I have such sights to show you, but don’t forget about this stuff – you never know when you might need to use it.
dplyr
We have already seen a bit of dplyr, but we are going to dive right into some of the functions now.
In base R, we have to do some chanting to select our variables. With dplyr, we can just use select:
mtcars %>%
select(mpg, cyl, am) mpg cyl am
Mazda RX4 21.0 6 1
Mazda RX4 Wag 21.0 6 1
Datsun 710 22.8 4 1
Hornet 4 Drive 21.4 6 0
Hornet Sportabout 18.7 8 0
Valiant 18.1 6 0
Duster 360 14.3 8 0
Merc 240D 24.4 4 0
Merc 230 22.8 4 0
Merc 280 19.2 6 0
Merc 280C 17.8 6 0
Merc 450SE 16.4 8 0
Merc 450SL 17.3 8 0
Merc 450SLC 15.2 8 0
Cadillac Fleetwood 10.4 8 0
Lincoln Continental 10.4 8 0
Chrysler Imperial 14.7 8 0
Fiat 128 32.4 4 1
Honda Civic 30.4 4 1
Toyota Corolla 33.9 4 1
Toyota Corona 21.5 4 0
Dodge Challenger 15.5 8 0
AMC Javelin 15.2 8 0
Camaro Z28 13.3 8 0
Pontiac Firebird 19.2 8 0
Fiat X1-9 27.3 4 1
Porsche 914-2 26.0 4 1
Lotus Europa 30.4 4 1
Ford Pantera L 15.8 8 1
Ferrari Dino 19.7 6 1
Maserati Bora 15.0 8 1
Volvo 142E 21.4 4 1We can also drop variables with the -:
mtcars %>%
select(-vs) mpg cyl disp hp drat wt qsec am gear carb
Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 1 4 4
Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 1 4 4
Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 4 1
Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 0 3 1
Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 3 2
Valiant 18.1 6 225.0 105 2.76 3.460 20.22 0 3 1
Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 3 4
Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 0 4 2
Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 0 4 2
Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 0 4 4
Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 0 4 4
Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 3 3
Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 3 3
Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 3 3
Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 3 4
Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 3 4
Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 3 4
Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 4 1
Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 4 2
Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 4 1
Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 0 3 1
Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 3 2
AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 3 2
Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 3 4
Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 3 2
Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 4 1
Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 1 5 2
Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 5 2
Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 1 5 4
Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 1 5 6
Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 1 5 8
Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 4 2
amFactor
Mazda RX4 1
Mazda RX4 Wag 1
Datsun 710 1
Hornet 4 Drive 0
Hornet Sportabout 0
Valiant 0
Duster 360 0
Merc 240D 0
Merc 230 0
Merc 280 0
Merc 280C 0
Merc 450SE 0
Merc 450SL 0
Merc 450SLC 0
Cadillac Fleetwood 0
Lincoln Continental 0
Chrysler Imperial 0
Fiat 128 1
Honda Civic 1
Toyota Corolla 1
Toyota Corona 0
Dodge Challenger 0
AMC Javelin 0
Camaro Z28 0
Pontiac Firebird 0
Fiat X1-9 1
Porsche 914-2 1
Lotus Europa 1
Ford Pantera L 1
Ferrari Dino 1
Maserati Bora 1
Volvo 142E 1We also have several helper functions that we can use:
HolzingerSwineford1939 %>%
select(num_range("x", 1:9), starts_with("age"),
matches("^s.*.l$")) x1 x2 x3 x4 x5 x6 x7 x8 x9
1 3.3333333 7.75 0.375 2.3333333 5.75 1.2857143 3.391304 5.75 6.361111
2 5.3333333 5.25 2.125 1.6666667 3.00 1.2857143 3.782609 6.25 7.916667
3 4.5000000 5.25 1.875 1.0000000 1.75 0.4285714 3.260870 3.90 4.416667
4 5.3333333 7.75 3.000 2.6666667 4.50 2.4285714 3.000000 5.30 4.861111
5 4.8333333 4.75 0.875 2.6666667 4.00 2.5714286 3.695652 6.30 5.916667
6 5.3333333 5.00 2.250 1.0000000 3.00 0.8571429 4.347826 6.65 7.500000
7 2.8333333 6.00 1.000 3.3333333 6.00 2.8571429 4.695652 6.20 4.861111
8 5.6666667 6.25 1.875 3.6666667 4.25 1.2857143 3.391304 5.15 3.666667
9 4.5000000 5.75 1.500 2.6666667 5.75 2.7142857 4.521739 4.65 7.361111
10 3.5000000 5.25 0.750 2.6666667 5.00 2.5714286 4.130435 4.55 4.361111
11 3.6666667 5.75 2.000 2.0000000 3.50 1.5714286 3.739130 5.70 4.305556
12 5.8333333 6.00 2.875 2.6666667 4.50 2.7142857 3.695652 5.15 4.138889
13 5.6666667 4.50 4.125 2.6666667 4.00 2.2857143 5.869565 5.20 5.861111
14 6.0000000 5.50 1.750 4.6666667 4.00 1.5714286 5.130435 4.70 4.444444
15 5.8333333 5.75 3.625 5.0000000 5.50 3.0000000 4.000000 4.35 5.861111
16 4.6666667 4.75 2.375 2.6666667 4.25 0.7142857 4.086957 3.80 5.138889
17 4.3333333 4.75 1.500 2.0000000 4.00 1.2857143 3.695652 6.65 5.250000
18 5.0000000 6.75 2.250 2.0000000 2.50 1.7142857 4.000000 5.25 5.444444
19 5.6666667 5.25 4.000 4.3333333 5.25 3.7142857 3.913044 4.85 5.750000
20 6.3333333 8.75 3.000 3.6666667 3.75 2.5714286 3.478261 5.35 4.916667
21 5.8333333 8.00 2.000 1.6666667 2.50 0.5714286 2.608696 4.60 5.388889
22 6.6666667 8.50 4.125 2.0000000 3.25 2.1428571 4.478261 5.45 7.000000
23 5.0000000 6.25 1.875 3.3333333 5.75 3.1428571 3.478261 4.60 5.000000
24 3.8333333 5.50 1.625 2.6666667 3.00 1.0000000 5.826087 5.30 6.777778
25 5.6666667 5.50 1.250 2.3333333 3.75 1.2857143 4.695652 4.60 4.138889
26 5.3333333 4.00 3.375 1.6666667 3.50 1.4285714 5.739130 6.25 4.333333
27 5.5000000 5.25 4.500 2.6666667 2.25 0.7142857 4.130435 5.10 4.527778
28 6.0000000 5.00 2.125 1.6666667 3.00 1.1428571 2.826087 5.55 4.416667
29 4.6666667 6.00 4.250 2.0000000 3.00 2.0000000 5.130435 5.85 8.611111
30 5.0000000 4.50 0.750 2.6666667 3.25 1.8571429 4.652174 4.85 5.444444
31 3.5000000 5.75 1.375 2.0000000 3.50 1.8571429 4.826087 6.95 5.972222
32 3.0000000 6.00 0.250 1.6666667 3.00 1.0000000 2.043478 3.65 3.361111
33 5.0000000 5.25 1.750 2.6666667 5.25 2.0000000 2.695652 4.30 4.805556
34 4.1666667 6.00 2.375 3.3333333 4.25 1.8571429 5.391304 4.35 5.638889
35 3.3333333 3.75 1.500 1.3333333 3.00 0.8571429 2.782609 5.20 4.833333
36 4.8333333 5.25 0.500 1.6666667 4.75 1.4285714 3.130435 3.75 4.916667
37 5.5000000 7.00 3.500 2.6666667 4.00 2.0000000 3.826087 4.00 5.305556
38 3.8333333 4.50 2.250 3.0000000 3.00 1.7142857 4.086957 3.50 5.083333
39 6.3333333 4.00 3.875 4.0000000 5.25 3.2857143 5.521739 5.45 5.111111
40 5.8333333 7.75 2.500 3.0000000 5.25 3.1428571 3.217391 4.50 4.888889
41 3.8333333 5.75 1.625 2.6666667 4.25 2.1428571 4.913043 5.10 4.638889
42 3.1666667 5.00 1.250 1.6666667 4.25 1.5714286 2.826087 5.30 4.777778
43 1.8333333 5.25 1.000 1.6666667 3.75 0.5714286 3.956522 4.75 2.777778
44 4.1666667 5.25 1.875 2.0000000 3.00 1.4285714 3.956522 5.60 6.666667
45 6.3333333 5.50 2.750 4.6666667 5.50 2.0000000 5.391304 5.00 6.861111
46 6.0000000 5.50 4.500 3.0000000 4.25 1.2857143 4.826087 5.00 5.000000
47 7.1666667 8.50 4.000 0.6666667 1.00 1.0000000 3.347826 6.35 6.277778
48 3.1666667 4.75 1.375 2.6666667 3.25 1.2857143 6.130435 8.00 5.444444
49 4.3333333 5.50 2.750 2.0000000 2.25 1.0000000 5.652174 5.90 6.055556
50 4.5000000 6.25 1.125 3.6666667 5.50 2.1428571 2.565217 4.80 5.527778
51 5.5000000 5.75 3.750 1.6666667 2.25 0.1428571 2.347826 5.05 5.500000
52 7.0000000 6.00 2.125 2.3333333 4.50 1.4285714 3.652174 5.15 4.777778
53 3.8333333 7.50 3.250 0.6666667 1.50 0.1428571 3.260870 4.20 5.388889
54 5.1666667 4.75 1.750 3.3333333 3.50 2.1428571 3.478261 5.10 4.194444
55 5.0000000 6.00 4.125 2.0000000 4.50 2.1428571 4.173913 4.80 4.416667
56 5.6666667 5.25 2.125 2.6666667 4.50 1.4285714 4.043478 5.70 5.555556
57 4.0000000 4.75 3.250 1.6666667 3.00 1.7142857 4.173913 5.25 5.638889
58 5.8333333 5.25 3.875 2.6666667 5.50 2.4285714 3.434783 5.80 4.750000
59 3.8333333 6.50 2.000 1.0000000 2.50 1.2857143 3.391304 4.55 4.833333
60 4.1666667 5.75 1.750 1.3333333 3.00 1.0000000 3.521739 6.15 3.944444
61 5.3333333 5.75 3.375 4.0000000 5.50 2.5714286 5.260870 6.20 6.138889
62 4.0000000 6.00 3.625 2.6666667 5.00 2.1428571 4.913043 5.35 4.777778
63 5.3333333 6.75 1.375 1.6666667 2.50 0.7142857 2.652174 3.85 5.333333
64 5.3333333 5.00 1.250 3.3333333 4.50 2.4285714 5.521739 5.45 5.833333
65 3.6666667 5.75 3.625 2.6666667 5.00 1.4285714 3.304348 4.50 5.027778
66 6.5000000 6.00 2.500 3.6666667 4.50 3.0000000 5.695652 5.40 6.305556
67 4.0000000 9.25 4.000 3.0000000 3.75 1.0000000 3.608696 5.75 6.194444
68 4.6666667 5.75 3.625 2.6666667 2.75 1.8571429 3.869565 6.10 4.250000
69 2.8333333 5.00 0.875 3.0000000 2.50 1.5714286 6.826087 5.70 3.916667
70 4.6666667 5.00 0.750 4.3333333 4.00 2.7142857 4.739130 5.95 5.416667
71 0.6666667 4.50 0.750 2.0000000 3.00 1.0000000 3.608696 5.50 4.611111
72 4.3333333 9.25 3.375 1.3333333 2.25 1.1428571 3.739130 5.75 5.166667
73 5.0000000 4.50 2.625 1.6666667 2.75 1.5714286 5.260870 7.35 5.972222
74 5.0000000 6.00 3.250 3.3333333 5.75 2.7142857 3.478261 4.60 4.277778
75 4.1666667 5.25 2.125 3.0000000 3.25 0.7142857 3.478261 5.70 4.583333
76 3.8333333 5.25 2.375 1.6666667 2.25 1.0000000 3.130435 5.75 4.666667
77 5.6666667 7.00 2.125 4.0000000 4.75 2.2857143 5.652174 5.70 6.472222
78 1.6666667 5.75 1.375 0.0000000 1.50 1.1428571 5.695652 4.00 5.638889
79 6.3333333 5.50 4.125 4.0000000 3.25 1.8571429 5.565217 7.35 5.750000
80 4.0000000 5.25 2.500 1.0000000 1.50 1.8571429 4.695652 5.15 5.333333
81 4.5000000 6.00 1.750 1.6666667 2.00 1.5714286 5.869565 6.45 6.027778
82 4.6666667 8.00 4.250 3.0000000 4.75 2.4285714 5.130435 5.75 5.305556
83 4.8333333 8.25 2.250 0.3333333 2.25 0.5714286 5.347826 5.20 5.777778
84 4.8333333 6.50 1.750 2.3333333 3.50 0.7142857 5.782609 5.75 4.972222
85 3.0000000 5.25 0.625 1.0000000 1.50 1.0000000 4.956522 4.85 4.583333
86 6.3333333 6.25 2.500 3.3333333 5.75 3.7142857 4.608696 6.85 5.472222
87 5.5000000 7.00 2.875 2.6666667 4.00 0.8571429 4.086957 5.40 5.972222
88 5.3333333 6.00 2.750 4.0000000 5.00 2.1428571 5.521739 4.55 5.138889
89 3.3333333 7.25 3.250 1.3333333 1.25 0.5714286 3.565217 5.55 4.888889
90 5.5000000 5.00 2.250 3.6666667 4.50 1.7142857 4.173913 5.95 6.666667
91 4.0000000 6.50 2.625 2.6666667 2.75 1.8571429 6.652174 7.50 5.444444
92 3.8333333 6.25 3.375 2.0000000 3.75 0.4285714 5.391304 7.80 6.111111
93 5.1666667 4.75 2.125 1.0000000 2.00 1.5714286 3.565217 6.40 5.722222
94 4.3333333 3.50 0.875 2.6666667 3.25 1.1428571 3.608696 4.80 3.944444
95 4.1666667 5.50 0.875 4.6666667 4.75 2.1428571 4.130435 5.35 3.777778
96 5.0000000 5.75 4.250 4.0000000 4.25 2.4285714 3.565217 3.60 5.444444
97 4.3333333 4.75 0.500 3.3333333 5.75 2.8571429 5.521739 5.85 4.222222
98 7.5000000 7.50 2.125 5.3333333 6.75 2.7142857 5.130435 5.55 7.222222
99 5.0000000 3.75 1.375 1.6666667 2.75 1.4285714 5.565217 6.10 4.611111
100 5.5000000 6.25 2.750 3.6666667 4.50 3.2857143 4.913043 5.15 5.750000
101 6.1666667 3.75 4.375 2.6666667 3.25 1.0000000 4.260870 5.30 6.250000
102 6.5000000 6.50 1.875 3.6666667 3.75 1.7142857 4.521739 4.40 6.583333
103 4.3333333 7.75 1.875 4.3333333 4.50 1.8571429 5.869565 6.25 4.111111
104 4.6666667 5.25 1.625 3.3333333 4.50 2.8571429 3.826087 4.85 4.833333
105 6.8333333 9.00 4.375 2.6666667 5.75 5.0000000 3.000000 6.20 6.027778
106 4.5000000 6.50 3.125 2.6666667 5.50 2.1428571 6.347826 6.50 6.166667
107 6.8333333 6.50 0.750 5.3333333 5.75 3.1428571 7.434783 5.70 5.194444
108 5.5000000 6.75 3.750 2.6666667 2.75 2.0000000 4.173913 6.80 7.000000
109 6.3333333 5.50 1.625 5.6666667 5.50 4.0000000 5.695652 6.40 7.527778
110 4.1666667 4.25 2.250 3.3333333 3.50 1.4285714 4.478261 4.15 3.361111
111 5.6666667 9.25 4.375 3.6666667 4.75 3.0000000 3.260870 3.90 4.861111
112 6.3333333 5.25 2.625 4.3333333 4.25 1.5714286 2.869565 6.00 5.444444
113 6.1666667 6.25 4.250 5.0000000 3.50 1.8571429 4.565217 5.35 5.444444
114 5.1666667 6.50 1.750 4.0000000 5.25 1.8571429 4.695652 4.30 6.000000
115 4.1666667 7.50 3.875 1.0000000 2.00 0.8571429 3.565217 3.95 6.333333
116 4.1666667 5.75 1.000 3.6666667 4.75 1.8571429 4.826087 5.85 5.416667
117 5.1666667 5.75 2.500 2.6666667 4.75 2.7142857 5.304348 6.85 5.000000
118 4.3333333 5.25 4.000 3.0000000 2.75 1.0000000 5.565217 6.60 6.444444
119 3.5000000 7.25 3.375 2.3333333 2.25 1.1428571 3.695652 5.20 5.166667
120 4.6666667 4.75 1.625 2.6666667 3.25 2.0000000 4.086957 5.55 5.444444
121 4.8333333 6.00 1.500 2.6666667 4.25 1.2857143 5.826087 6.40 6.861111
122 5.0000000 5.50 2.375 3.3333333 3.00 2.0000000 4.608696 6.40 3.305556
123 7.5000000 7.00 4.250 4.0000000 6.50 3.5714286 3.739130 7.60 6.500000
124 5.3333333 5.25 4.125 2.3333333 3.75 1.5714286 3.652174 5.35 4.777778
125 6.1666667 6.75 4.125 3.3333333 5.00 2.8571429 5.000000 6.90 6.388889
126 5.3333333 8.75 3.125 4.3333333 4.00 1.1428571 4.000000 6.95 5.666667
127 4.3333333 7.00 1.000 4.3333333 5.50 3.0000000 5.130435 5.65 4.916667
128 4.8333333 7.00 1.125 3.3333333 5.00 2.2857143 4.913043 5.25 4.972222
129 6.0000000 7.50 3.250 3.0000000 6.00 2.4285714 3.304348 5.10 5.777778
130 5.0000000 4.50 1.625 2.0000000 2.75 0.5714286 4.521739 6.25 6.305556
131 4.1666667 8.00 4.375 4.3333333 6.25 3.1428571 4.565217 7.80 7.000000
132 5.6666667 5.50 3.500 4.0000000 4.25 2.2857143 7.260870 6.35 7.194444
133 5.0000000 6.25 1.750 1.3333333 2.00 0.5714286 4.913043 6.00 4.805556
134 3.5000000 5.25 2.250 2.0000000 3.75 1.8571429 4.695652 5.25 3.722222
135 7.3333333 8.00 2.625 2.6666667 5.00 2.4285714 3.434783 6.00 6.166667
136 6.1666667 7.50 3.625 4.0000000 6.25 2.5714286 4.391304 5.85 6.111111
137 4.8333333 5.25 4.500 4.3333333 5.75 2.8571429 3.347826 5.10 5.444444
138 5.6666667 6.25 2.750 3.3333333 5.25 2.1428571 4.434783 5.15 4.555556
139 5.5000000 6.75 4.500 2.3333333 4.50 2.5714286 6.260870 6.55 6.888889
140 5.1666667 5.00 2.500 3.3333333 5.75 3.0000000 6.434783 8.30 7.083333
141 3.1666667 3.75 1.500 3.3333333 5.75 2.2857143 6.043478 5.25 6.222222
142 5.0000000 7.50 4.500 2.0000000 1.50 0.4285714 3.304348 5.25 5.722222
143 7.1666667 9.00 3.875 3.6666667 5.25 4.7142857 3.826087 7.10 5.777778
144 7.3333333 6.75 4.000 6.0000000 6.50 6.1428571 5.347826 5.75 6.611111
145 2.0000000 5.50 0.625 2.6666667 5.00 0.8571429 2.391304 5.60 5.972222
146 3.8333333 5.50 1.875 3.6666667 5.00 3.0000000 5.608696 4.90 3.861111
147 4.1666667 6.00 1.250 4.0000000 5.00 2.5714286 6.956522 6.25 6.305556
148 4.6666667 5.75 1.625 0.6666667 2.50 1.4285714 4.521739 5.00 4.750000
149 5.8333333 4.75 2.625 5.6666667 5.50 4.1428571 3.565217 6.30 5.472222
150 6.6666667 5.50 4.375 2.6666667 3.75 1.0000000 5.130435 4.75 5.222222
151 6.8333333 7.25 4.250 5.0000000 5.75 4.8571429 5.652174 7.55 6.166667
152 5.3333333 4.75 2.625 3.0000000 5.50 2.1428571 5.782609 7.90 6.944444
153 4.8333333 5.00 2.375 3.0000000 4.25 2.4285714 5.391304 7.50 5.416667
154 5.1666667 6.00 2.375 1.3333333 2.25 1.1428571 5.391304 6.15 5.194444
155 6.3333333 6.75 1.125 3.0000000 2.50 1.4285714 4.695652 5.60 4.138889
156 4.8333333 5.75 1.250 3.0000000 4.75 2.1428571 3.608696 6.15 4.694444
157 3.8333333 4.75 0.500 3.3333333 4.25 1.4285714 3.000000 4.10 4.333333
158 5.5000000 5.50 2.125 2.6666667 4.25 1.4285714 2.826087 4.90 5.416667
159 5.6666667 6.00 2.750 3.6666667 4.75 2.7142857 2.173913 4.30 6.333333
160 4.8333333 5.75 1.125 3.0000000 4.75 1.5714286 4.956522 5.15 4.000000
161 2.6666667 6.25 1.250 2.6666667 6.25 3.4285714 4.869565 6.10 4.444444
162 5.0000000 6.25 2.500 3.3333333 5.75 2.5714286 4.086957 5.65 5.583333
163 6.0000000 8.25 4.500 5.6666667 6.25 5.8571429 5.608696 6.95 9.250000
164 4.6666667 6.25 1.125 3.3333333 4.50 1.5714286 4.173913 4.75 4.833333
165 5.0000000 6.25 1.375 3.6666667 5.25 1.1428571 4.478261 5.70 5.472222
166 3.3333333 6.25 0.750 3.0000000 5.25 2.2857143 3.869565 5.05 4.944444
167 4.5000000 6.50 0.750 3.3333333 4.00 1.8571429 3.826087 5.35 3.805556
168 5.3333333 5.25 1.000 0.3333333 1.75 1.5714286 4.478261 6.80 4.277778
169 6.3333333 7.75 1.500 3.3333333 2.75 2.0000000 3.608696 5.40 5.583333
170 2.8333333 5.25 0.750 1.6666667 2.50 1.4285714 4.304348 4.35 4.083333
171 5.6666667 7.00 3.000 4.6666667 5.50 3.7142857 2.130435 4.20 4.750000
172 4.1666667 7.75 2.250 2.3333333 3.00 1.5714286 2.826087 4.00 3.472222
173 5.5000000 7.75 3.750 3.6666667 5.75 2.5714286 2.869565 5.65 5.166667
174 6.6666667 5.75 2.500 3.3333333 5.75 5.0000000 3.130435 5.20 6.166667
175 5.0000000 5.50 2.500 2.6666667 4.25 2.8571429 4.130435 5.50 4.472222
176 6.0000000 7.00 2.750 4.3333333 6.00 5.1428571 3.565217 5.15 5.694444
177 4.0000000 4.00 1.750 1.6666667 4.25 1.5714286 4.608696 4.00 3.277778
178 6.6666667 6.50 3.250 4.3333333 6.00 3.5714286 3.826087 6.05 6.250000
179 5.0000000 6.00 2.375 4.6666667 6.50 3.4285714 4.869565 5.75 5.138889
180 7.0000000 6.75 3.375 2.3333333 3.25 0.5714286 5.478261 10.00 6.555556
181 5.5000000 6.75 2.000 2.6666667 4.25 1.8571429 2.956522 5.80 6.083333
182 5.3333333 5.50 1.875 3.0000000 5.00 2.4285714 3.217391 5.90 5.305556
183 5.1666667 5.25 0.625 4.3333333 4.75 2.7142857 4.173913 6.05 5.000000
184 4.5000000 5.75 0.500 3.0000000 2.75 1.0000000 2.391304 5.90 4.944444
185 5.1666667 5.75 1.375 1.3333333 4.00 2.2857143 3.521739 6.40 5.250000
186 5.1666667 8.50 0.375 3.0000000 4.75 2.4285714 2.217391 4.60 5.055556
187 2.8333333 7.50 1.625 3.0000000 4.25 1.8571429 2.260870 4.70 3.972222
188 5.0000000 5.00 1.625 3.0000000 5.00 3.0000000 4.695652 5.65 5.000000
189 4.6666667 4.75 1.000 3.0000000 3.50 2.8571429 3.521739 5.80 4.416667
190 3.1666667 5.50 1.000 1.6666667 3.00 0.5714286 2.173913 3.60 4.500000
191 4.6666667 5.00 1.750 2.6666667 3.75 1.1428571 4.347826 7.20 5.694444
192 6.3333333 6.25 1.625 3.0000000 5.75 2.1428571 2.434783 6.50 5.500000
193 5.6666667 7.00 1.250 3.0000000 5.50 2.8571429 3.521739 4.80 5.527778
194 3.0000000 5.50 0.625 0.6666667 1.00 0.2857143 1.304348 3.05 3.111111
195 2.6666667 5.00 1.000 2.0000000 4.50 1.8571429 4.043478 5.55 5.138889
196 3.0000000 7.50 2.125 6.3333333 6.00 4.7142857 4.000000 5.40 4.111111
197 5.3333333 5.25 1.125 5.0000000 5.00 3.5714286 4.130435 4.60 4.944444
198 5.6666667 5.25 1.125 3.0000000 5.75 3.4285714 2.521739 4.55 4.805556
199 3.5000000 5.50 1.000 3.0000000 3.00 1.1428571 2.826087 4.20 3.805556
200 4.6666667 5.00 1.750 2.6666667 4.50 1.4285714 2.652174 5.00 5.944444
201 6.5000000 6.00 3.125 4.6666667 4.25 1.5714286 3.565217 5.20 6.777778
202 5.3333333 6.50 1.250 3.6666667 5.75 3.2857143 2.695652 4.15 3.972222
203 4.6666667 6.00 1.000 2.0000000 2.50 1.4285714 2.652174 3.85 4.416667
204 4.0000000 5.00 2.750 3.6666667 4.75 2.5714286 3.086956 4.70 4.277778
205 5.1666667 4.75 1.625 2.6666667 5.50 2.4285714 2.652174 3.50 3.333333
206 4.8333333 6.50 3.125 3.3333333 5.50 2.5714286 3.695652 6.40 5.611111
207 4.8333333 7.50 1.875 2.3333333 4.00 1.7142857 2.782609 3.70 4.583333
208 2.6666667 5.75 0.625 2.3333333 5.00 1.8571429 4.130435 6.40 3.805556
209 4.1666667 6.25 3.250 1.6666667 1.75 0.7142857 2.000000 3.60 3.361111
210 4.1666667 6.75 1.875 2.0000000 4.00 1.8571429 3.739130 4.95 5.944444
211 6.1666667 7.75 2.000 4.6666667 7.00 2.8571429 3.826087 5.70 6.194444
212 5.0000000 6.50 2.375 2.3333333 5.25 2.0000000 3.869565 6.05 6.166667
213 4.8333333 6.00 1.250 3.0000000 5.25 2.4285714 4.347826 6.05 5.722222
214 6.1666667 8.50 2.125 6.0000000 6.00 3.8571429 3.478261 5.60 6.361111
215 4.6666667 5.00 0.500 2.6666667 4.50 0.8571429 3.173913 4.20 4.472222
216 3.6666667 8.50 2.375 3.3333333 4.25 2.1428571 3.478261 5.05 5.138889
217 6.3333333 5.25 2.250 6.0000000 6.50 4.4285714 5.217391 5.45 5.694444
218 4.8333333 5.25 2.250 2.3333333 4.00 1.0000000 2.913044 4.40 5.000000
219 4.1666667 6.25 3.750 3.0000000 4.00 2.2857143 4.608696 6.35 4.861111
220 4.6666667 6.75 1.625 1.6666667 1.50 0.5714286 4.391304 5.30 4.777778
221 3.8333333 5.00 2.250 2.0000000 3.00 0.8571429 1.869565 5.00 4.027778
222 1.8333333 5.00 1.125 4.3333333 4.00 2.1428571 3.173913 3.65 3.611111
223 7.5000000 9.25 3.625 3.3333333 4.00 2.2857143 3.173913 5.05 6.111111
224 3.1666667 3.75 0.875 5.0000000 4.75 2.7142857 4.391304 5.60 3.222222
225 6.8333333 5.25 1.375 3.0000000 4.00 2.0000000 5.391304 5.95 6.111111
226 5.8333333 7.50 4.125 2.6666667 3.75 1.7142857 3.913044 6.30 6.722222
227 5.6666667 6.00 2.000 3.0000000 3.50 1.4285714 3.869565 5.80 6.555556
228 3.1666667 5.50 1.500 3.3333333 4.00 2.4285714 5.130435 5.80 7.000000
229 4.1666667 5.25 1.875 2.6666667 4.25 2.4285714 2.956522 4.10 4.722222
230 6.0000000 7.00 4.125 5.0000000 6.00 5.5714286 3.521739 5.20 5.833333
231 3.1666667 5.75 0.750 2.3333333 3.25 2.7142857 2.956522 4.85 4.138889
232 4.5000000 5.25 0.875 3.0000000 4.75 3.1428571 3.826087 5.45 5.305556
233 3.5000000 2.25 1.750 5.0000000 6.25 4.2857143 2.956522 4.55 5.027778
234 4.5000000 5.50 4.000 2.6666667 3.25 1.8571429 2.434783 3.75 4.916667
235 4.3333333 5.50 1.000 1.6666667 2.75 1.5714286 3.304348 5.70 4.333333
236 3.3333333 6.75 1.875 3.0000000 4.75 1.5714286 5.652174 5.25 6.694444
237 5.5000000 5.50 1.750 4.3333333 6.25 3.7142857 3.652174 6.35 6.388889
238 6.3333333 6.50 0.875 5.3333333 6.25 2.1428571 4.739130 5.55 5.555556
239 5.5000000 6.25 4.250 5.0000000 5.75 3.0000000 4.739130 7.15 6.833333
240 6.0000000 7.25 2.000 3.0000000 5.75 3.2857143 6.478261 7.80 6.861111
241 6.3333333 7.25 4.375 4.3333333 5.50 2.4285714 4.869565 6.30 6.305556
242 5.1666667 6.25 3.500 3.3333333 6.25 3.8571429 4.478261 4.90 4.666667
243 6.0000000 7.00 1.625 3.6666667 5.75 2.5714286 5.826087 5.10 6.222222
244 5.1666667 6.50 3.625 3.6666667 6.50 1.7142857 3.695652 4.95 5.250000
245 4.6666667 6.00 0.750 2.6666667 4.25 2.1428571 4.000000 4.75 5.972222
246 6.3333333 9.25 3.500 3.3333333 4.75 2.7142857 4.782609 6.75 5.527778
247 4.8333333 8.50 2.750 3.3333333 5.00 2.7142857 3.652174 6.60 4.083333
248 5.8333333 6.00 1.875 4.0000000 5.00 3.2857143 4.000000 6.25 6.444444
249 5.8333333 6.25 3.125 3.6666667 6.00 2.7142857 5.739130 5.90 5.194444
250 3.8333333 5.25 0.375 3.0000000 5.25 1.7142857 5.782609 5.55 6.527778
251 5.1666667 7.00 3.125 4.0000000 5.75 2.1428571 6.043478 5.50 5.527778
252 8.5000000 6.50 4.250 6.0000000 6.50 5.4285714 5.782609 8.05 6.916667
253 5.5000000 7.00 2.250 5.0000000 5.75 4.2857143 4.173913 6.10 5.888889
254 3.5000000 6.50 2.125 4.0000000 4.00 4.7142857 5.130435 5.60 3.666667
255 6.1666667 8.00 1.375 5.3333333 6.25 4.5714286 3.478261 4.75 4.750000
256 6.1666667 5.00 2.625 2.6666667 4.75 2.7142857 3.391304 5.05 4.972222
257 6.1666667 6.50 3.625 2.3333333 4.75 2.7142857 4.434783 5.65 5.833333
258 6.5000000 6.50 3.000 5.6666667 6.50 4.2857143 5.000000 6.80 7.388889
259 6.5000000 8.50 4.125 3.3333333 4.75 2.2857143 4.130435 5.95 6.666667
260 3.0000000 4.00 0.500 3.3333333 5.25 2.7142857 2.956522 4.00 3.472222
261 4.6666667 7.00 2.250 3.3333333 6.25 3.2857143 3.782609 4.65 4.722222
262 4.8333333 5.75 1.125 2.0000000 6.00 1.2857143 4.347826 9.10 6.305556
263 4.1666667 5.00 1.375 4.0000000 4.75 2.4285714 4.826087 6.25 5.722222
264 4.8333333 8.25 1.375 4.3333333 5.75 3.7142857 3.391304 5.15 5.500000
265 5.3333333 5.25 1.875 4.6666667 5.00 4.1428571 5.086957 5.40 6.583333
266 5.0000000 5.25 2.625 4.0000000 6.00 3.8571429 4.173913 5.65 5.722222
267 5.8333333 7.00 2.375 6.0000000 6.75 4.7142857 6.304348 5.85 6.277778
268 2.6666667 8.50 4.000 4.6666667 5.50 3.4285714 4.304348 5.40 5.972222
269 6.3333333 7.50 4.125 4.6666667 5.50 4.1428571 4.217391 6.00 7.000000
270 4.3333333 6.25 0.875 3.3333333 3.75 1.8571429 5.000000 6.45 5.083333
271 5.5000000 7.00 1.500 4.6666667 5.25 2.0000000 4.608696 5.30 5.194444
272 4.6666667 6.75 4.000 3.3333333 4.75 2.4285714 3.000000 6.50 5.500000
273 4.5000000 5.50 2.000 2.6666667 4.75 2.1428571 5.869565 7.10 6.250000
274 4.3333333 7.25 1.250 2.6666667 4.75 1.8571429 3.695652 5.45 6.111111
275 5.0000000 8.00 3.250 2.3333333 3.75 1.4285714 4.739130 7.00 4.944444
276 3.6666667 5.75 1.000 1.3333333 3.25 2.4285714 4.000000 4.05 4.166667
277 5.3333333 6.00 1.000 3.0000000 4.75 2.0000000 3.391304 4.45 5.305556
278 5.1666667 5.75 1.625 4.0000000 4.75 2.1428571 3.565217 5.40 5.055556
279 5.3333333 6.25 2.125 1.6666667 2.75 2.2857143 4.608696 7.15 5.555556
280 6.6666667 5.25 1.875 2.6666667 4.50 1.8571429 3.652174 6.30 5.972222
281 3.5000000 5.00 1.375 2.3333333 4.75 1.1428571 3.478261 5.85 6.527778
282 5.1666667 6.25 3.250 5.0000000 6.00 3.2857143 2.391304 4.00 4.277778
283 4.0000000 6.00 2.000 2.6666667 4.50 1.7142857 3.347826 4.70 3.750000
284 6.8333333 6.25 1.875 4.0000000 5.25 2.7142857 2.782609 4.70 5.250000
285 5.0000000 5.75 1.250 2.6666667 3.50 1.7142857 4.260870 6.60 6.666667
286 5.8333333 5.00 2.000 3.3333333 4.00 1.4285714 3.478261 5.25 5.694444
287 5.6666667 6.75 2.125 4.3333333 6.25 4.5714286 3.347826 5.95 5.416667
288 4.1666667 5.50 1.625 2.3333333 4.00 1.5714286 5.869565 6.30 5.666667
289 4.0000000 6.25 0.750 3.0000000 4.75 3.2857143 5.217391 6.55 5.722222
290 6.0000000 6.50 2.125 3.3333333 4.75 1.4285714 2.434783 5.75 5.000000
291 3.3333333 4.75 0.875 2.6666667 5.00 0.8571429 5.826087 5.50 6.777778
292 4.6666667 6.00 1.125 1.3333333 3.00 1.5714286 4.173913 5.75 4.833333
293 5.6666667 5.50 1.625 3.3333333 4.25 2.0000000 5.478261 6.00 4.500000
294 5.6666667 5.25 2.375 3.3333333 4.50 2.0000000 3.391304 5.15 6.333333
295 5.8333333 7.00 1.250 3.0000000 3.25 1.5714286 4.173913 4.85 5.777778
296 6.1666667 6.50 3.000 3.0000000 4.25 2.8571429 3.043478 4.25 5.666667
297 4.0000000 7.00 1.375 2.6666667 4.25 1.0000000 5.086957 5.60 5.250000
298 3.0000000 6.00 1.625 2.3333333 4.00 1.0000000 4.608696 6.05 6.083333
299 4.6666667 5.50 1.875 3.6666667 5.75 4.2857143 4.000000 6.00 7.611111
300 4.3333333 6.75 0.500 3.6666667 4.50 2.0000000 5.086957 6.20 4.388889
301 4.3333333 6.00 3.375 3.6666667 5.75 3.1428571 4.086957 6.95 5.166667
ageyr agemo school
1 13 1 Pasteur
2 13 7 Pasteur
3 13 1 Pasteur
4 13 2 Pasteur
5 12 2 Pasteur
6 14 1 Pasteur
7 12 1 Pasteur
8 12 2 Pasteur
9 13 0 Pasteur
10 12 5 Pasteur
11 12 2 Pasteur
12 12 11 Pasteur
13 12 7 Pasteur
14 12 8 Pasteur
15 12 6 Pasteur
16 12 1 Pasteur
17 14 11 Pasteur
18 13 5 Pasteur
19 12 8 Pasteur
20 12 3 Pasteur
21 14 10 Pasteur
22 12 9 Pasteur
23 12 11 Pasteur
24 12 8 Pasteur
25 12 3 Pasteur
26 12 7 Pasteur
27 12 8 Pasteur
28 13 2 Pasteur
29 12 5 Pasteur
30 12 2 Pasteur
31 12 7 Pasteur
32 16 0 Pasteur
33 12 2 Pasteur
34 12 3 Pasteur
35 13 3 Pasteur
36 13 10 Pasteur
37 12 9 Pasteur
38 12 8 Pasteur
39 12 6 Pasteur
40 12 5 Pasteur
41 12 1 Pasteur
42 13 6 Pasteur
43 13 8 Pasteur
44 14 8 Pasteur
45 14 2 Pasteur
46 13 7 Pasteur
47 13 5 Pasteur
48 13 6 Pasteur
49 12 11 Pasteur
50 13 2 Pasteur
51 13 7 Pasteur
52 12 4 Pasteur
53 15 7 Pasteur
54 13 4 Pasteur
55 12 8 Pasteur
56 14 4 Pasteur
57 16 2 Pasteur
58 13 3 Pasteur
59 14 0 Pasteur
60 15 3 Pasteur
61 12 5 Pasteur
62 12 9 Pasteur
63 12 10 Pasteur
64 13 11 Pasteur
65 13 1 Pasteur
66 12 11 Pasteur
67 14 11 Pasteur
68 13 0 Pasteur
69 13 9 Pasteur
70 12 8 Pasteur
71 14 2 Pasteur
72 13 3 Pasteur
73 13 1 Pasteur
74 13 7 Pasteur
75 12 9 Pasteur
76 13 9 Pasteur
77 12 6 Pasteur
78 16 7 Pasteur
79 14 7 Pasteur
80 14 1 Pasteur
81 14 11 Pasteur
82 13 7 Pasteur
83 14 5 Pasteur
84 13 2 Pasteur
85 14 7 Pasteur
86 12 11 Pasteur
87 13 8 Pasteur
88 13 3 Pasteur
89 13 11 Pasteur
90 13 10 Pasteur
91 13 10 Pasteur
92 14 0 Pasteur
93 15 4 Pasteur
94 13 8 Pasteur
95 14 10 Pasteur
96 13 8 Pasteur
97 13 4 Pasteur
98 13 2 Pasteur
99 13 11 Pasteur
100 13 4 Pasteur
101 15 3 Pasteur
102 13 10 Pasteur
103 13 3 Pasteur
104 13 4 Pasteur
105 15 3 Pasteur
106 12 10 Pasteur
107 13 5 Pasteur
108 13 10 Pasteur
109 14 5 Pasteur
110 13 3 Pasteur
111 13 4 Pasteur
112 13 1 Pasteur
113 13 4 Pasteur
114 14 0 Pasteur
115 14 5 Pasteur
116 13 1 Pasteur
117 16 0 Pasteur
118 13 10 Pasteur
119 13 4 Pasteur
120 16 5 Pasteur
121 14 4 Pasteur
122 15 1 Pasteur
123 14 4 Pasteur
124 15 8 Pasteur
125 14 5 Pasteur
126 15 4 Pasteur
127 13 11 Pasteur
128 13 11 Pasteur
129 13 4 Pasteur
130 14 1 Pasteur
131 13 11 Pasteur
132 14 1 Pasteur
133 15 3 Pasteur
134 13 6 Pasteur
135 14 7 Pasteur
136 13 4 Pasteur
137 13 10 Pasteur
138 13 2 Pasteur
139 14 2 Pasteur
140 14 7 Pasteur
141 14 0 Pasteur
142 14 9 Pasteur
143 15 0 Pasteur
144 12 9 Pasteur
145 15 8 Pasteur
146 13 6 Pasteur
147 13 8 Pasteur
148 15 8 Pasteur
149 14 4 Pasteur
150 15 1 Pasteur
151 13 11 Pasteur
152 15 5 Pasteur
153 14 1 Pasteur
154 15 1 Pasteur
155 15 7 Pasteur
156 15 6 Pasteur
157 13 0 Grant-White
158 11 10 Grant-White
159 12 6 Grant-White
160 11 11 Grant-White
161 12 5 Grant-White
162 12 6 Grant-White
163 12 8 Grant-White
164 11 11 Grant-White
165 12 5 Grant-White
166 12 5 Grant-White
167 12 0 Grant-White
168 12 10 Grant-White
169 12 9 Grant-White
170 12 8 Grant-White
171 12 9 Grant-White
172 13 1 Grant-White
173 12 1 Grant-White
174 13 1 Grant-White
175 12 7 Grant-White
176 12 1 Grant-White
177 12 9 Grant-White
178 12 8 Grant-White
179 12 6 Grant-White
180 14 0 Grant-White
181 12 3 Grant-White
182 12 4 Grant-White
183 12 9 Grant-White
184 14 7 Grant-White
185 13 2 Grant-White
186 12 5 Grant-White
187 12 0 Grant-White
188 12 0 Grant-White
189 12 6 Grant-White
190 13 2 Grant-White
191 12 0 Grant-White
192 12 10 Grant-White
193 11 11 Grant-White
194 13 8 Grant-White
195 12 7 Grant-White
196 12 4 Grant-White
197 12 6 Grant-White
198 12 6 Grant-White
199 12 1 Grant-White
200 12 9 Grant-White
201 12 3 Grant-White
202 12 4 Grant-White
203 12 10 Grant-White
204 12 5 Grant-White
205 11 11 Grant-White
206 12 8 Grant-White
207 11 11 Grant-White
208 14 1 Grant-White
209 12 4 Grant-White
210 13 2 Grant-White
211 12 3 Grant-White
212 12 11 Grant-White
213 11 5 Grant-White
214 12 4 Grant-White
215 12 0 Grant-White
216 13 11 Grant-White
217 12 4 Grant-White
218 12 9 Grant-White
219 12 10 Grant-White
220 13 7 Grant-White
221 13 2 Grant-White
222 14 0 Grant-White
223 12 11 Grant-White
224 13 0 Grant-White
225 12 8 Grant-White
226 12 3 Grant-White
227 12 0 Grant-White
228 13 2 Grant-White
229 12 7 Grant-White
230 11 4 Grant-White
231 14 0 Grant-White
232 12 9 Grant-White
233 12 5 Grant-White
234 12 9 Grant-White
235 12 7 Grant-White
236 14 2 Grant-White
237 13 1 Grant-White
238 12 11 Grant-White
239 13 2 Grant-White
240 13 6 Grant-White
241 13 9 Grant-White
242 13 2 Grant-White
243 13 1 Grant-White
244 13 8 Grant-White
245 14 2 Grant-White
246 13 8 Grant-White
247 13 6 Grant-White
248 13 7 Grant-White
249 13 3 Grant-White
250 12 10 Grant-White
251 13 5 Grant-White
252 14 6 Grant-White
253 14 9 Grant-White
254 15 11 Grant-White
255 13 9 Grant-White
256 13 1 Grant-White
257 13 9 Grant-White
258 13 7 Grant-White
259 13 0 Grant-White
260 13 8 Grant-White
261 12 9 Grant-White
262 14 10 Grant-White
263 13 5 Grant-White
264 13 4 Grant-White
265 13 6 Grant-White
266 13 6 Grant-White
267 13 5 Grant-White
268 12 1 Grant-White
269 13 5 Grant-White
270 13 2 Grant-White
271 13 7 Grant-White
272 15 3 Grant-White
273 13 3 Grant-White
274 14 4 Grant-White
275 14 7 Grant-White
276 13 3 Grant-White
277 13 8 Grant-White
278 14 6 Grant-White
279 14 9 Grant-White
280 16 4 Grant-White
281 12 11 Grant-White
282 13 1 Grant-White
283 14 1 Grant-White
284 14 3 Grant-White
285 14 9 Grant-White
286 16 1 Grant-White
287 13 5 Grant-White
288 14 3 Grant-White
289 13 1 Grant-White
290 14 4 Grant-White
291 15 6 Grant-White
292 14 11 Grant-White
293 12 11 Grant-White
294 14 3 Grant-White
295 13 0 Grant-White
296 13 3 Grant-White
297 13 5 Grant-White
298 14 10 Grant-White
299 14 3 Grant-White
300 14 2 Grant-White
301 13 5 Grant-WhiteNot Important, But Helpful
Changing variable position in R is a pain:
head(HolzingerSwineford1939[, c(1, 7:15, 2:6)]) id x1 x2 x3 x4 x5 x6 x7 x8 x9
1 1 3.333333 7.75 0.375 2.333333 5.75 1.2857143 3.391304 5.75 6.361111
2 2 5.333333 5.25 2.125 1.666667 3.00 1.2857143 3.782609 6.25 7.916667
3 3 4.500000 5.25 1.875 1.000000 1.75 0.4285714 3.260870 3.90 4.416667
4 4 5.333333 7.75 3.000 2.666667 4.50 2.4285714 3.000000 5.30 4.861111
5 5 4.833333 4.75 0.875 2.666667 4.00 2.5714286 3.695652 6.30 5.916667
6 6 5.333333 5.00 2.250 1.000000 3.00 0.8571429 4.347826 6.65 7.500000
sex ageyr agemo school grade
1 1 13 1 Pasteur 7
2 2 13 7 Pasteur 7
3 2 13 1 Pasteur 7
4 1 13 2 Pasteur 7
5 2 12 2 Pasteur 7
6 2 14 1 Pasteur 7HolzingerSwineford1939 %>%
select(id, starts_with("x"), everything()) %>%
head() id x1 x2 x3 x4 x5 x6 x7 x8 x9
1 1 3.333333 7.75 0.375 2.333333 5.75 1.2857143 3.391304 5.75 6.361111
2 2 5.333333 5.25 2.125 1.666667 3.00 1.2857143 3.782609 6.25 7.916667
3 3 4.500000 5.25 1.875 1.000000 1.75 0.4285714 3.260870 3.90 4.416667
4 4 5.333333 7.75 3.000 2.666667 4.50 2.4285714 3.000000 5.30 4.861111
5 5 4.833333 4.75 0.875 2.666667 4.00 2.5714286 3.695652 6.30 5.916667
6 6 5.333333 5.00 2.250 1.000000 3.00 0.8571429 4.347826 6.65 7.500000
sex ageyr agemo school grade
1 1 13 1 Pasteur 7
2 2 13 7 Pasteur 7
3 2 13 1 Pasteur 7
4 1 13 2 Pasteur 7
5 2 12 2 Pasteur 7
6 2 14 1 Pasteur 7Your Turn!
Use that Stata test file.
Grab every lvi, effect, leader, and cred variable
Use summary to understand your data.
Now, just keep every lvi variable.
Use a corrplot to see relationships.
- corrplot needs a correlation matrix (use cor)
install.packages("corrplot")Subsetting/Filtering
One of the more frequent tasks is related to filtering/subsetting your data. You often want to impose some types of rules on your data (e.g., US only, date ranges).
Base
R gives us all the ability in the world to filter data.
summary(mtcars[mtcars$mpg < mean(mtcars$mpg), ]) mpg cyl disp hp
Min. :10.40 Min. :6.000 Min. :145.0 Min. :105.0
1st Qu.:14.78 1st Qu.:8.000 1st Qu.:275.8 1st Qu.:156.2
Median :15.65 Median :8.000 Median :311.0 Median :180.0
Mean :15.90 Mean :7.556 Mean :313.8 Mean :191.9
3rd Qu.:18.02 3rd Qu.:8.000 3rd Qu.:360.0 3rd Qu.:226.2
Max. :19.70 Max. :8.000 Max. :472.0 Max. :335.0
drat wt qsec vs
Min. :2.760 Min. :2.770 Min. :14.50 Min. :0.0000
1st Qu.:3.070 1st Qu.:3.440 1st Qu.:16.10 1st Qu.:0.0000
Median :3.150 Median :3.570 Median :17.35 Median :0.0000
Mean :3.302 Mean :3.839 Mean :17.10 Mean :0.1667
3rd Qu.:3.600 3rd Qu.:3.844 3rd Qu.:17.94 3rd Qu.:0.0000
Max. :4.220 Max. :5.424 Max. :20.22 Max. :1.0000
am gear carb amFactor
Min. :0.0000 Min. :3.000 Min. :1.000 0:15
1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.250 1: 3
Median :0.0000 Median :3.000 Median :4.000
Mean :0.1667 Mean :3.444 Mean :3.556
3rd Qu.:0.0000 3rd Qu.:3.750 3rd Qu.:4.000
Max. :1.0000 Max. :5.000 Max. :8.000 Unless you know exactly what you are doing, this is a bit hard to read – you might be asking yourself what the comma means and why there is nothing after it.
dplyr
When we use filter, we are specifying what it is that we want to keep.
Filter this or that:
mtcars %>%
filter(cyl == 4 | cyl == 8) %>%
summary() mpg cyl disp hp
Min. :10.40 Min. :4.00 Min. : 71.1 Min. : 52.0
1st Qu.:15.20 1st Qu.:4.00 1st Qu.:120.1 1st Qu.: 93.0
Median :18.70 Median :8.00 Median :275.8 Median :150.0
Mean :20.19 Mean :6.24 Mean :244.0 Mean :153.5
3rd Qu.:24.40 3rd Qu.:8.00 3rd Qu.:351.0 3rd Qu.:205.0
Max. :33.90 Max. :8.00 Max. :472.0 Max. :335.0
drat wt qsec vs
Min. :2.76 Min. :1.513 Min. :14.50 Min. :0.0
1st Qu.:3.08 1st Qu.:2.320 1st Qu.:16.90 1st Qu.:0.0
Median :3.69 Median :3.435 Median :17.60 Median :0.0
Mean :3.60 Mean :3.245 Mean :17.81 Mean :0.4
3rd Qu.:4.08 3rd Qu.:3.780 3rd Qu.:18.61 3rd Qu.:1.0
Max. :4.93 Max. :5.424 Max. :22.90 Max. :1.0
am gear carb amFactor
Min. :0.0 Min. :3.00 Min. :1.00 0:15
1st Qu.:0.0 1st Qu.:3.00 1st Qu.:2.00 1:10
Median :0.0 Median :3.00 Median :2.00
Mean :0.4 Mean :3.64 Mean :2.64
3rd Qu.:1.0 3rd Qu.:4.00 3rd Qu.:4.00
Max. :1.0 Max. :5.00 Max. :8.00 Filter this and that:
mtcars %>%
filter(cyl == 4 & mpg > 25) %>%
summary() mpg cyl disp hp
Min. :26.00 Min. :4 Min. : 71.10 Min. : 52.00
1st Qu.:28.07 1st Qu.:4 1st Qu.: 76.45 1st Qu.: 65.25
Median :30.40 Median :4 Median : 78.85 Median : 66.00
Mean :30.07 Mean :4 Mean : 86.65 Mean : 75.50
3rd Qu.:31.90 3rd Qu.:4 3rd Qu.: 91.08 3rd Qu.: 84.75
Max. :33.90 Max. :4 Max. :120.30 Max. :113.00
drat wt qsec vs
Min. :3.770 Min. :1.513 Min. :16.70 Min. :0.0000
1st Qu.:4.080 1st Qu.:1.670 1st Qu.:17.30 1st Qu.:1.0000
Median :4.150 Median :1.885 Median :18.71 Median :1.0000
Mean :4.252 Mean :1.873 Mean :18.40 Mean :0.8333
3rd Qu.:4.378 3rd Qu.:2.089 3rd Qu.:19.33 3rd Qu.:1.0000
Max. :4.930 Max. :2.200 Max. :19.90 Max. :1.0000
am gear carb amFactor
Min. :1 Min. :4.000 Min. :1.0 0:0
1st Qu.:1 1st Qu.:4.000 1st Qu.:1.0 1:6
Median :1 Median :4.000 Median :1.5
Mean :1 Mean :4.333 Mean :1.5
3rd Qu.:1 3rd Qu.:4.750 3rd Qu.:2.0
Max. :1 Max. :5.000 Max. :2.0 Filter this out:
mtcars %>%
filter(cyl != 4) %>%
summary() mpg cyl disp hp
Min. :10.40 Min. :6.000 Min. :145.0 Min. :105.0
1st Qu.:15.00 1st Qu.:6.000 1st Qu.:225.0 1st Qu.:123.0
Median :16.40 Median :8.000 Median :301.0 Median :175.0
Mean :16.65 Mean :7.333 Mean :296.5 Mean :180.2
3rd Qu.:19.20 3rd Qu.:8.000 3rd Qu.:360.0 3rd Qu.:215.0
Max. :21.40 Max. :8.000 Max. :472.0 Max. :335.0
drat wt qsec vs
Min. :2.760 Min. :2.620 Min. :14.50 Min. :0.0000
1st Qu.:3.070 1st Qu.:3.435 1st Qu.:16.46 1st Qu.:0.0000
Median :3.150 Median :3.520 Median :17.30 Median :0.0000
Mean :3.348 Mean :3.705 Mean :17.17 Mean :0.1905
3rd Qu.:3.730 3rd Qu.:3.840 3rd Qu.:17.98 3rd Qu.:0.0000
Max. :4.220 Max. :5.424 Max. :20.22 Max. :1.0000
am gear carb amFactor
Min. :0.0000 Min. :3.000 Min. :1.000 0:16
1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000 1: 5
Median :0.0000 Median :3.000 Median :4.000
Mean :0.2381 Mean :3.476 Mean :3.476
3rd Qu.:0.0000 3rd Qu.:4.000 3rd Qu.:4.000
Max. :1.0000 Max. :5.000 Max. :8.000 Naturally, it can also take a function
mtcars %>%
filter(mpg < mean(mpg)) %>%
summary() mpg cyl disp hp
Min. :10.40 Min. :6.000 Min. :145.0 Min. :105.0
1st Qu.:14.78 1st Qu.:8.000 1st Qu.:275.8 1st Qu.:156.2
Median :15.65 Median :8.000 Median :311.0 Median :180.0
Mean :15.90 Mean :7.556 Mean :313.8 Mean :191.9
3rd Qu.:18.02 3rd Qu.:8.000 3rd Qu.:360.0 3rd Qu.:226.2
Max. :19.70 Max. :8.000 Max. :472.0 Max. :335.0
drat wt qsec vs
Min. :2.760 Min. :2.770 Min. :14.50 Min. :0.0000
1st Qu.:3.070 1st Qu.:3.440 1st Qu.:16.10 1st Qu.:0.0000
Median :3.150 Median :3.570 Median :17.35 Median :0.0000
Mean :3.302 Mean :3.839 Mean :17.10 Mean :0.1667
3rd Qu.:3.600 3rd Qu.:3.844 3rd Qu.:17.94 3rd Qu.:0.0000
Max. :4.220 Max. :5.424 Max. :20.22 Max. :1.0000
am gear carb amFactor
Min. :0.0000 Min. :3.000 Min. :1.000 0:15
1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.250 1: 3
Median :0.0000 Median :3.000 Median :4.000
Mean :0.1667 Mean :3.444 Mean :3.556
3rd Qu.:0.0000 3rd Qu.:3.750 3rd Qu.:4.000
Max. :1.0000 Max. :5.000 Max. :8.000 Your Turn
For now, we are going to stick with that stataExample data.
Select the same variables, but also include Rater.
Filter the data on Rater – check the values and filter both ways.
Now check those correlations again!
Throw the Gender variable in and filter on that.
New Variables and Recoding
Base
Adding a new variable in base R is as easy as the following:
mtcars$roundedMPG = round(mtcars$mpg)dplyr
If, however, we want to do things in a tidy chunk, we need to use mutate.
mtcars = mtcars %>%
mutate(roundedMPG = round(mpg))There is also transmute. Can anyone venture a guess as to what it might do?
Base Recoding
You will need to recode variables at some point. Depending on the nature of the recode it can be easy (e.g., to reverse code a scale, you just subtract every value by max value + 1).
You will need to do some more elaborate stuff:
mtcars$mpgLoHi = 0
mtcars$mpgLoHi[mtcars$mpg > median(mtcars$mpg)] = 1mtcars$mpgLoHi = ifelse(mtcars$mpg > median(mtcars$mpg), 1, 0)These are pretty good ways to do recoding of this nature, but what about this:
mtcars$vs[which(mtcars$vs == 0)] = "v"
mtcars$vs[which(mtcars$vs == 1)] = "s"Or this:
mtcars$vs = ifelse(mtcars$vs == 0, "v", "s")dplyr recoding
recode(mtcars$vs, `0` = "v", `1` = "s")Communication
We won’t have any big end-of-day wrap exercises to do today. Instead, we are going to learn just a few cool things.
ggplot2
We already saw some ggplot2, but let’s take a few minutes to dive into a bit more.
Just like everything else in the tidyverse, ggplot2 provides a clear and consistent grammar, except the focus is on data visualization. With ggplot2, we can stack layer after layer into the plotting space to help visualize our data.
Let’s take a look at some good ggplot2 layering:
library(ggplot2)
library(lavaan)
testData = HolzingerSwineford1939
ggplot(testData, aes(x7, ageyr)) +
geom_point()
Next, we can add some color:
ggplot(testData, aes(x7, ageyr)) +
geom_point(aes(color = as.factor(grade)), alpha = .75)
Now, we can add a smooth line:
ggplot(testData, aes(x7, ageyr)) +
geom_point(aes(color = as.factor(grade)), alpha = .75) +
geom_smooth()
And we can look at small multiples:
ggplot(testData, aes(x7, ageyr)) +
geom_point(aes(color = as.factor(grade)), alpha = .75) +
geom_smooth() +
facet_grid(~ sex)
Let’s get those silly grey boxes out of there:
ggplot(testData, aes(x7, ageyr)) +
geom_point(aes(color = as.factor(grade)), alpha = .75) +
geom_smooth() +
facet_grid(~ sex) +
theme_minimal()
Perhaps add a better color scheme:
ggplot(testData, aes(x7, ageyr)) +
geom_point(aes(color = as.factor(grade)), alpha = .75) +
geom_smooth() +
facet_grid(~ sex) +
theme_minimal() +
scale_color_brewer(palette = "Dark2")
We could keep going forever and tweak anything that you could imagine (labels, ticks, etc.), but this should give you a pretty good idea about what you can do with regard to static plots.
Oh…but we don’t have to stick with just static plots. We can use the plotly package to make our ggplot object interactive.
library(plotly)
radPlot = ggplot(testData, aes(x7, ageyr)) +
geom_point(aes(color = as.factor(grade)), alpha = .75) +
geom_smooth() +
facet_grid(~ sex) +
theme_minimal() +
scale_color_brewer(palette = "Dark2")
ggplotly(radPlot)You can also build plots with plotly, but we will save that for another day in the future.
DT
Visualizations are great and they often tell a better story than tables. Sometimes, though, you want to give people a glimpse of the data. The DT package let’s you create interactive data tables (they are JS data tables).
You could give people the entire data to explore:
library(DT)
datatable(testData)You can also use the DT package to tidy your summaries into a nice dataframe:
lm(x7 ~ ageyr + school, data = testData) %>%
broom::tidy() %>%
mutate_if(is.numeric, round, 4) %>%
datatable()We don’t want to get too far ahead of ourselves here – we will see more places to use this tomorrow.
R Markdown & Knitr
Do you have a moment to hear the good word of Donald Knuth? If you want to work in a reproducible fashion base and knitr